Question: ${\sqrt[3]{1024} = \text{?}}$
$\sqrt[3]{1024}$ is the number that, when multiplied by itself three times, equals $1024$ First break down $1024$ into its prime factorization and look for factors that appear three times. So the prime factorization of $1024$ is $2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$ Notice that we can rearrange the factors like so: $1024 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = (2\times 2\times 2) \times (2\times 2\times 2) \times (2\times 2\times 2) \times 2$ So $\sqrt[3]{1024} = \sqrt[3]{2\times 2\times 2} \times \sqrt[3]{2\times 2\times 2} \times \sqrt[3]{2\times 2\times 2} \times \sqrt[3]{2}$ $\sqrt[3]{1024} = 2\times 2\times 2 \times \sqrt[3]{2}$ $\sqrt[3]{1024} = 8 \sqrt[3]{2}$